Why am I getting a small bandgap in density of states of graphene?

[Shan]

Dear QW experts,

I have test simulated graphene (2 atoms) for the band gap and DOS. I observed a small band gap from the density of states plot.

I have attached the python script and the obtained DOS plot for your reference.

Please point, where am I doing wrong?

[zh]

The k-mesh size is too coarse. You need to increase it for the geometry optimization and DOS calculations.

"bands_above_fermi_level=None," in the DOS calculations should not be "None".

[Shan]

I have increased the k-points to 24*24*1.
and considered 40 bands above the fermi level.

Still, the problem persists.

[Petr Khomyakov]

You should shift the k-grid to the G point, and make sure that the grid chosen also includes the K-point, as this is the point where the graphene conduction and valence bands touch. Regarding DOS calculation for graphene, you may take a look at Appendix in Phys. Rev. B 87, 075414 (2013).

[Shan]

It's easy to say someone to refer to some paper. Well, its a good thing and I appreciate your suggestion.

However, to get the zero band gap in the DOS, all i need to do finally will be definitely changing the parameters or theory. I have taken the converged parameters for the calculation, still I am getting the issue. You should have pointed out the problem and convey where the issue was. 

Even if i read the whole paper u referred, I won't be able to know what values of k-points and mess cutoff i have to choose to get the accurate result.
 I appreciate your suggestion (reference paper) and I am on it, but plz try to identify the issue instead of skipping it.

[Petr Khomyakov]

As you may see in my original post, I have not suggested reading the entire paper, but a rather tiny Appendix, which has all the information about the k-meshes that can be adopted for accurate calculation of graphene's DOS (not for self-consistent calculation).  The choice of the mesh is up to you, as you are the master of your research. As I said in the original reply, the k-grid should include the K-symmetry point since this is where the conduction and valence bands touch, and the DOS has a gap because the k-mesh is too coarse as pointed out by zh.   

[Shan]

Dear sir,

I went through the appendix of the article.

I tried several k-points and combinations, but the problem still exists.
I also used dense 288*288*1 k-points for both SCF and DOS in the code attached below, still I am getting a small band gap when I zoomed the plot to -1 to 1 eV range.

The code and the plot are attached below.

Please suggest... I am exhausted from my side.

[Petr Khomyakov]

What version of ATK are you using? I guess the problem is that your k-mesh does not include K-symmetry point, and that is crucial to avoid an artificial band gap opening (due to the use of relatively coarse grid) in the graphene's band structure.

Having the 288x288 k-point grid does not guarantee that the K-point is a grid point. In the ATK-2016.4 (as well as in the VASP code adopted for the calculations in the paper mentioned), there is an option "Shift to G-point", in this case the the 288x288 k-point grid would include K-symmetry point indeed. 

If you have an old version of ATK, you may adopt an odd k-point grid that includes not only Gamma-point, but also the K-point, e.g., the 27x27 (129x129) k-point grid for self-consistent (DOS) calculation. It worked for me.

[Daniele Stradi]

We have investigated the problem and it seems to be a potential bug in the way the DOS is plotted in VNL. Plotting the dos using a script based on the script "si_dos_plot.py" provided in

http://docs.quantumwise.com/manuals/Types/DensityOfStates/DensityOfStates.html

gives a correct DOS for graphene with a vanishing DOS at E_F. I attach the adapted script here, it plots both the DOS using the tetrahedron method (more precise, but require fine sampling) and the DOS using a gaussian smearing (which works with a coarser sampling).

I attach both the script and the resulting DOS.

Regards,
Daniele.

[Shan]

Dear Dr. Daniel,
   The code u suggested produces no different plot than the VNL. I request you, to verify your plot for an energy range of -1eV to 1ev, coz the very small band gap can't be seen in a wide energy window.

Dear Dr.Petr,
I used the version 2014.3.
Yes, the 129*129 k-grid worked for me, while the 27*27 didn't. However, the plot produced from 129*129 grid is little uncomfortable to deal with. please find the attached DOS for 129*129 grid over a wide energy range and its zoomed version. 

[Petr Khomyakov]

I meant using the 27x27 k-point mesh for self-consistent calculation, not DOS. But as you may see in the figure enclosed, the 27x27 grid is not that bad, at least it does not open the energy gap in the graphene's DOS.

Enclosed you can find graphene's DOS calculated in ATK-2016.4, using the 129x129 k-point mesh for DOS calculations. It looks perfectly fine.

So, I cannot say right away if that is a bug in ATK-2014.3 version. If so, it has certainly been fixed in newer versions of ATK. 

[Shan]

Ok...
thank you Dr. petr